Nuprl Lemma : fpf-rename-dom
∀[A,C:Type]. ∀[B:A ─→ Type].
∀eqa:EqDecider(A). ∀eqc:EqDecider(C). ∀r:A ─→ C. ∀f:a:A fp-> B[a]. ∀c:C.
(↑c ∈ dom(rename(r;f)) ⇐⇒ ∃a:A. ((↑a ∈ dom(f)) c∧ (c = (r a) ∈ C)))
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
exists_wf,
l_member_wf,
member_map,
map_wf,
iff_wf,
assert_wf,
deq-member_wf,
equal_wf
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type].
\mforall{}eqa:EqDecider(A). \mforall{}eqc:EqDecider(C). \mforall{}r:A {}\mrightarrow{} C. \mforall{}f:a:A fp-> B[a]. \mforall{}c:C.
(\muparrow{}c \mmember{} dom(rename(r;f)) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:A. ((\muparrow{}a \mmember{} dom(f)) c\mwedge{} (c = (r a))))
Date html generated:
2015_07_17-AM-11_10_41
Last ObjectModification:
2015_01_28-AM-07_44_24
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